計算訓練集中的資料與訓練集中每個資料的距離（之後為測試集中每個資料找出訓練集中離它距離最小的k個）
用第二種方法，向量化計算距離的效率高

  def compute_distances_two_loops(self, X):
    """
    Compute the distance between each test point in X and each training point
self.X_train is training data and the 
   X is test data.

    Inputs:
    - X: A numpy array of shape (num_test, D)((500,3072)) containing test data.
self.X_train :(5000,3072)
    Returns:
    - dists: A numpy array of shape (num_test, num_train) ((500,5000))where dists[i, j]
      is the Euclidean distance between the ith test point and the jth training
      point.
    """
 

    num_test = X.shape[0]
    num_train = self.X_train.shape[0]
    dists = np.zeros((num_test, num_train))
    for i in range(num_test):
      for j in range(num_train):
        dist = np.sqrt(np.sum(np.square(X[i] - self.X_train[j])))
        dists[i, j] = dist
    return dists
    
  def compute_distances_no_loops
 
(self, X):
    """
    Compute the distance between each test point in X and each training point
    in self.X_train using no explicit loops.

    Input / Output: Same as compute_distances_two_loops
    """
    num_test = X.shape[0]
    num_train = self.X_train.shape[0]
    dists = np.zeros((num_test, num_train)
 
) 

    #formulate the l2 distance using matrix multiplication    #
  
    M = np.dot(X, self.X_train.T)
    print(X.shape, self.X_train.shape)
    print(M.shape)
    nrow, ncol = M.shape[0], M.shape[1]
    te = np.diag(np.dot(X, X.T))#the element on digonal is quardratic sum of every vector of X
    tr = np.diag(np.dot(self.X_train, self.X_train.T))
    te = np.reshape(np.repeat(te, ncol), M.shape)#copy M.shape times
    tr = np.reshape(np.repeat(tr, nrow), M.T.shape)
    distance_square = -2 * M + te + tr.T
    dists = np.sqrt(distance_square)
    return dists